I need to show that the function f(x)=|x|^1/2 is uniformly continuous on R. I know how to start it's just I get confused when it gets to f(x)-f(y). Any help would be appreciated.

What have you tried? What can you use?

If you're allowed to use anything I'd note that on is continuous and thus by the Heine-Cantor theorem uniformly continuous. Then, for I'd note that is bounded and thus is Lipschitz and so evidently unif. cont.